Polytope of Type {8,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*960b
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 80, 240, 60
Order of s0s1s2 : 20
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 1920
Vertex Figure Of :
   {2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*480
   4-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   8-fold quotients : {4,6}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*1920b, {8,12}*1920c, {8,6}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 2.
      30 facets:
         30 of {8}*16
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 3.
      20 facets:
         20 of {8}*16
      32 vertex figures:
         24 of {6}*12
         8 of {2}*4
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 6.
      10 facets:
         10 of {8}*16
      16 vertex figures:
         12 of {6}*12
         4 of {2}*4

Permutation Representation (GAP) : 
s0 := ( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);;
s1 := ( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)(12,35)(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)(25,51)(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)(52,64)(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);;
s2 := ( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)(10,80)(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)(27,43)(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)(40,50)(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(80)!( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);
s1 := Sym(80)!( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)(12,35)(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)(25,51)(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)(52,64)(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);
s2 := Sym(80)!( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)(10,80)(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)(27,43)(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)(40,50)(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);
poly := sub<Sym(80)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 >;
References : None.
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